How can I duplicate the vertices of an edge to move it without affecting surrounding edges?
I don't know if there is a one step solution, but aside from just manually doing everything I think the new extend edge tool (&#9095; AltV) is about the closest to a one-step as anything I can think of:



Note that the selection is extended towards the initial position of the mouse when &#9095; AltV is pressed, which can be confusing before you get used to it.



That said, I think in your particular situation I would do something more like this: